Write as a Single Logarithm log base b of 4+ log base b of x-3-4 log base b of y

$\log_{b} (4) + \log_{b} (x - 3) - 4 \log_{b} (y)$

Step 1

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log_{b} (4 (x - 3)) - 4 \log_{b} (y)$

Step 2

Simplify each term.

Apply the distributive property.

$\log_{b} (4 x + 4 \cdot - 3) - 4 \log_{b} (y)$

Multiply $4$ by $- 3$ .

$\log_{b} (4 x - 12) - 4 \log_{b} (y)$

Simplify $- 4 \log_{b} (y)$ by moving $4$ inside the logarithm.

$\log_{b} (4 x - 12) - \log_{b} (y^{4})$

Step 3

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log_{b} (\frac{4 x - 12}{y^{4}})$

Step 4

Factor $4$ out of $4 x - 12$ .

Factor $4$ out of $4 x$ .

$\log_{b} (\frac{4 (x) - 12}{y^{4}})$

Factor $4$ out of $- 12$ .

$\log_{b} (\frac{4 x + 4 \cdot - 3}{y^{4}})$

Factor $4$ out of $4 x + 4 \cdot - 3$ .

$\log_{b} (\frac{4 (x - 3)}{y^{4}})$